Question: Solve for $x$ and $y$ using elimination. ${4x+6y = 82}$ ${3x-5y = -5}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $-3$ and the bottom equation by $4$ ${-12x-18y = -246}$ $12x-20y = -20$ Add the top and bottom equations together. $-38y = -266$ $\dfrac{-38y}{{-38}} = \dfrac{-266}{{-38}}$ ${y = 7}$ Now that you know ${y = 7}$ , plug it back into $\thinspace {4x+6y = 82}\thinspace$ to find $x$ ${4x + 6}{(7)}{= 82}$ $4x+42 = 82$ $4x+42{-42} = 82{-42}$ $4x = 40$ $\dfrac{4x}{{4}} = \dfrac{40}{{4}}$ ${x = 10}$ You can also plug ${y = 7}$ into $\thinspace {3x-5y = -5}\thinspace$ and get the same answer for $x$ : ${3x - 5}{(7)}{= -5}$ ${x = 10}$